For now, she is best known as the daughter of Vanessa Paradis and Johnny Depp, but the signs are there that Instagram It-girl Lily-Rose will soon outshine them

It was 1990, Vanessa Paradis featured in her first advertising campaign for Chanel. She was cast as an exotic bird with a huge black plumed tail, sitting slightly crouched over a giant bottle of Chanel Coco perfume, a red cuff and chain attached to her ankle.

It was 1990, Vanessa Paradis featured in her first advertising campaign for Chanel. She was cast as an exotic bird with a huge black plumed tail, sitting slightly crouched over a giant bottle of Chanel Coco perfume, a red cuff and chain attached to her ankle.

Paradis was 19 when she struck that pose and began an enduring relationship that saw her become a muse to Karl Lagerfeld. In fact, the relationship endures to such an extent that it's now a family affair.

Lily-Rose Depp, Paradis's 17-year-old daughter with ex-partner Johnny Depp, has become the face of Chanel's new No5 L'Eau.

The campaign photo is evocative of Paradis's 1990, now classic ad. Lily-Rose not only has her mother's deep-set, heavy-lidded eyes and pouting expression, but she sits on a stool, in black but bare-shouldered, slightly crouched over a giant bottle of No5 L'Eau, a fresh, lively twist on the classic for the millennial woman.

Life moves on, fashion changes, classics need a tweak and younger models are required and yet, there is consistency, continuity. And so, the daughter, a slightly different woman to her mother, takes the reins. It's nice, it's neat, it seems like a natural passing of the baton, and the effect is as stunning as it was in 1990.

It's not much more than a year since Lily-Rose Depp began making A-list waves in her own right, and the L'Eau campaign is her second for Chanel with a relatively low-key eye shadow job under her double-C belt already.

Growing up in France, the daughter of one of its most famous women and of a huge Hollywood actor, she lived a relatively low-key life. This was a deliberate move on her parents' part. Paradis and Depp both knew well the downsides of celebrity. Paradis became famous at the age of 14, with her Lolita-ish pop hit, Joe le Taxi, and Depp was burned by the fame early on, when his bad-boy ways came in for a lot of scrutiny.

Depp didn't enjoy prying eyes and he never wanted to be a conventional star, so when he fell for Paradis, in the late 1990s, part of the pleasure of settling down was doing so in France, where his kids, Lily-Rose and her younger brother Jack, got to be relatively ordinary kids.

Well, relatively. You don't grow up around movie sets and singing backing vocals on your mother's albums without absorbing a bit of the hunger for the magic that comes with both. And, it would seem, Lily-Rose has that hunger.

Last year, she made her movie debut in Tusk, directed by Kevin Smith, father of her friend, Harley Quinn Smith, and he also directed her, along with Depp, in Yoga Hosers.

In interviews, Depp, who always spoke carefully about his kids and usually in the context of protecting their privacy, said that he was taken by surprise by Lily-Rose's move in to the spotlight. And, to some extent, her choice to move in to it.

After Lily-Rose appeared in Vogue last year, Depp said in an interview: "To be honest, I'm quite worried. I wasn't expecting all this to happen to Lily-Rose, especially not at this age. But it's her passion, and she's having fun. She knows I'm always there for her."

Depp's surprise was based on his own hopes for his daughter, of course, a case of "do what I say, not what I do", perhaps. He told her the world of fame and spotlights was bad and yet he and Paradis continued to inhabit it. In a way, of course his daughter wanted a bit of it for herself.

Being a child of the 21st Century, however, the first steps Lily-Rose Depp made into a public profile were on social media. With 2.1m followers on Instagram, it is here and on Vine that she has been making impact for years. Impossibly photogenic, with a great eye for composition, visual humour and wry observation, she has been the girl-crush of stylish young women for several years before her big ad campaigns and movie roles.

Lily-Rose is possessed, naturally, of great fashion sense and it shows on her Instagram. She knows how to put outfits together that look like she trawls vintage stores, the high street and her mother's couture, but then, of course, Lily-Rose has couture of her own these days.

Her role in Smith's Yoga Hosers might have been small, but Lily-Rose attended the Sundance Festival premiere in Chanel.

There is an ongoing sense of deja-vu; as it is almost like watching her mother all over again, but then, Lily-Rose Depp is very much her own woman. Possibly as a result of her upbringing and partly due to that very modern social-media outlet for self-expression that goes beyond how her parents' world works.

It was on Instagram that Lily-Rose Depp made her feelings felt about the fallout from her father's separation from Amber Heard earlier this year.

"My dad is the sweetest most loving person I know, he's been nothing but a wonderful father to my little brother and I, and everyone who knows him would say the same," she wrote in May, defending her father against Heard's allegations of domestic abuse.

If that particular situation and the reporting of it was distressing for Depp and Heard, it must have been doubly so for his teenage kids, no matter how worldly they are.

It was reported that Lily-Rose's mother, Paradis, was going to make a deposition in defence of her ex, but it never came to that in the end. For any teenager, it would be a difficult experience, and, perhaps, the idea of ploughing one's one furrow through fame, through all of that, was a pleasant distraction for Lily-Rose.

Almost to a person, celebrities will say that they would not recommend their life to their children. And yet, it is often the case that children of celebrities will follow similar paths to their parents. Whether it's simply that they choose to inhabit a world that is familiar to them, or that they have similar artistic leanings, or both, the children's fortunes can be mixed.

Growing up the child of successful actors or musicians or models does not guarantee similar success for the offspring. Sometimes, the kids can have all the talent and good looks and charm of their parents, but they just don't have that special ingredient that makes a star.

Vanessa Paradis and Lily-Rose Depp's Chanel perfume poses were struck decades apart and yet, there is a quality to them that is timeless. It's that star quality, that elusive X ingredient that can't be faked.